Question

Identify the properties of the following illustrations. a) 0.326 b) 0.5\overline{4} c) 0.326

Decimals
ANSWERED
asked 2021-06-06
Identify the properties of the following illustrations.
a) 0.326
b) \(0.5\overline{4}\)
c) 0.326

Answers (1)

2021-06-07
Step 1
a) Consider the given decimal number,
0.326
Here the objective is to find the properties of the given decimal number.
The decimal number is divided into three types.
1.Terminating decimals.
2. Recurring Decimals.
3. Irrational numbers.
it can be observed that there 3 finite digits after the decimal point. so, it is a Terminating decimal number. it can be written in fraction form,
\(0.326=\frac{326}{1000}\)
\(=\frac{163}{500}\)
Step 2
b) Consider the given decimal number,
\(0.5\overline{4}\)
Here the objective is to find the properties of the given decimal number.
The decimal number is divided into three types.
1.Terminating decimals.
2. Recurring Decimals.
3. Irrational numbers.
it can be observed that 4 is repeating continuously up to infinite. so, it is a Recurring decimal number. it can be written in fraction form,
\(100x=54.4444444444\ \cdots\ \cdots\)
\(-x=0.4444444444\ \cdots\ \cdots\)
\(99x=54\)
\(x=\frac{6}{11}\)
Step 3
c) Consider the given decimal number,
0.326
Here the objective is to find the properties of the given decimal number.
The decimal number is divided into three types.
1.Terminating decimals.
2. Recurring Decimals.
3. Irrational numbers.
it can be observed that 4 is repeating continuously up to infinite. so, it is a Recurring decimal number. it can be written in fraction form,
\(100x=54.4444444444\ \cdots\ \cdots\)
\(-x=0.4444444444\ \cdots\ \cdots\)
\(99x=54\)
\(x=\frac{6}{11}\)
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